Question regarding Voltage/Potential dividers I know the basic concepts about the formula and how does a voltage divider work but I can't seem to know why we should use it? Conceptually explaining why is more helpful rather than just citing practical applications about it though it can be used as a visual to provide more understanding.
 A: The most immediately obvious physical utility of a voltage divider is that, by adjusting the relative proportion of the two resistances (for a resistive divider), you can tone down the voltage to any number ranging from zero, to a maximum = voltage value you feed into the divider arrangement. 
Since $$V_{\rm (across \ R_2)} = V_{\rm (applied)} \left( \frac{R_2}{R_1 + R_2} \right)$$
Now imagine, if we keep vary $R_1$ and $R_2$ in a manner such that their sum is kept the same (e.g. the combinations [$1k, 9k$], [$2k, 8k$], [$3k, 7k$] etc.), in each case, voltage across $R_2$ is also changing in steps of $V_{\rm applied}/10$. The step size can always be altered, simply by changing the relative proportion. 
Now. if this voltage across $R_2$ is passed onto some secondary circuit, you have complete control over the voltage that drives the other circuit (through the resistance proportion). Thus, you can influence the output of the secondary circuit simply by controlling this relative proportion of resistances. 
The applications of this idea can be diverse - from creating a variable voltage supply from a fixed high voltage, to practical stuff like regulators for appliances (e.g. take a fan, passing lesser voltage/power, implies that the output is toned down proportionately, fan speed can be controlled). In circuitry, you need this as an important circuit component, to give calculated voltage biases, such as in a voltage comparator circuit using an operational amplifier (one of the many possible applications) and in generating timing waveforms (using e.g. an astable multivibrator). Dividers are also important parts of the circuit in digital-analog conversion circuits (which make use of voltage-divider ladder circuits) etc. There can be more sophisticated applications too (which probably your book has listed.)
In each case, the basic idea remains the same. Controlling voltage by adjusting the relative proportion of resistances.
